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Home COVID-19 Garbage in, garbage out – bogus maths behind the R number

Garbage in, garbage out – bogus maths behind the R number

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THE official government website defines the virus reproduction number R as ‘the average number of secondary infections produced by a single infected person. An R number of 1 means that on average every person who is infected will infect 1 other person, meaning the total number of infections is stable’.   

This basic concept is now widely understood throughout the UK, and the mainstream media always give prominence to the announcement of new R number calculations (one for each region). R numbers above 1 are invariably used by politicians to justify ever more authoritarian and destructive measures. But not one of them has the wit to demand: ‘Explain to me precisely how the latest set of R numbers has been calculated.’   

Gov.uk states: ‘Different modelling groups use different data sources to estimate these values using mathematical models that simulate the spread of infections.’ But what exactly does that mean? It sounds suspiciously like spreadsheets and guesswork. 

To get to the bottom of the maths it is imperative to consider the R number concept from first principles and not be bamboozled by academic flatulence. The alternative is to behave exactly like the majority of our bovine MPs and simply accept whatever we are told as the truth – just like the moronic and oft-repeated mantra from Johnson, Hancock et al that they are ‘following the science’.  

The good news is that the maths is not difficult. Imagine a small island with 2,500 inhabitants. On a particular Friday, ten of them take a day trip off the island and return infected with a virus. After that point no else comes or goes. Therefore, on the very first day, there are ten people infected. 

Now assume that there is a testing regime in place where every Friday evening, all 2,500 islanders are tested and all the results are available by midnight. Then, assuming all the tests are accurate, the data will be transparent, incontrovertible and complete. 

Assume that the first set of tests is conducted a week after the infected ten return from their day trip, and the tests still reveal ten people to be positive. According to the government definition this would imply an R number of 1 (‘on average every person who is infected will infect 1 other person’) but this is not necessarily true. It is possible that the infected ten have not infected anyone at all but they are still ill to some extent and testing positive. Alternatively, each of the first ten might have infected one other person and then recovered to test negative. On our hypothetical island, this would in fact be crystal clear because it would be possible to identify every  person and their test result. 

The same principle would apply if the first evening of mass testing resulted in 20 people returning positive results. Now there would be a significant increase in cases – the total has in fact doubled, suggesting an R number of 2. This would be of concern because if the total doubled every week, then it would take only about eight weeks before the entire island was stricken (20-40-80-160-320-640-1,280-2,560) and supposedly ‘overwhelmed’. Unless of course the actual symptoms were mild and tolerable for most. 

Such scary modelling! But this is just primary school maths and not remotely representative of reality because, as mentioned above, the basic R number calculation does not account for the recovery period and other pertinent factors. 

If it was the case that the average recovery period was exactly one week, and each of the original ten cases had infected two others (and all ten had recovered by the time of the mass testing), then that would imply a genuine R number of 2.0 (20 new cases in the community after the initial ten). And potentially the same impact during the second week where the 20 each infected another two people (40) – but all 20 also recovered, with the expectation of 80 new cases in the following week. 

Again, the basic maths predicts disaster for the island, especially if new cases start to include the elderly and vulnerable. But in fact, the infection sequence is highly unlikely to be that bad because each week, all those who had recovered (also doubling every week in that simplistic sequence) would be steadily rejoining the island community and building up a pool of immune folk. This would leave a reducing number of susceptible people, many of whom would be taking sensible precautions. And what would be even better is if the average recovery period was less than a week, because people might catch the virus, recover swiftly, join the immune pool and reduce any opportunity to infect others. 

In fact, authorities on the hypothetical island would always be in a very powerful position because every Friday midnight they would know not only the exact number of infections but the identity of every single case. Having this precise and reliable information, regularly available on a weekly basis, would make infection control a doddle. It would be so straightforward to isolate all the infected persons and quickly minimise the risks of further transmissions on top of sensible precautions, such as shielding the vulnerable. 

Unfortunately, this hypothetical island scenario is not remotely realistic in terms of the UK situation but this has not stopped the Sage academics from playing with their spreadsheets, despite a paucity of reliable input data. And finding innovative ways to estimate an R number for each region, which is then regarded as factual by the Government and the mainstream media. 

To reiterate, here are the various issues that prevent R numbers from being anything better than informed guesses: 

  • Regular testing (and prompt result reporting) for 67million people is utterly impracticable. 
  • The PCR tests, used widely across the UK, have become notorious for returning high numbers of false positives. 
  • No account is taken of the recovery period, which for many  (not just the young) can be very swift e.g. Donald Trump, the Prince of Wales.
  • No account is taken of the rapidly growing proportion of people, especially the young, who have recovered and have a level of immunity. 
  • No account is taken of the lethality of the virus – mild cases are not excess deaths. 

There is an accepted term for this in computing: GIGO – garbage in, garbage out. The logical implications are that the official R number calculations cannot be trusted and should definitely never be used as the justification for more draconian lockdowns that destroy lives and livelihoods. 

Because without hard verifiable data to input and process, all Professor Ferguson and his Sage colleagues ever do is play around with their ‘models’. With invariably pessimistic results, because they always catch media attention, startle ministers like rabbits in headlights and feed the lockdown narrative. And it is not as if the hypocritical professor has not got any ‘previous’ for this scare-mongering. His record is quite astonishing. Foot-and-mouth, BSE (mad cow disease), bird flu and swine flu. All were predicted by Ferguson and colleagues to result in tens of thousands of deaths; the reality was hundreds. 

And finally, I suggest you give plenty of thought to the calculations that are being used to determine the official Covid infection rate for each county/area. Or perhaps not if you are depressed enough. What I believe to be happening (because there is no rational alternative) is that in each area, the proportion of positive to negative test results is being compared, and then scaled up. For example, if in Kent 10,000 people are tested and 50 are found to be positive, then the whole of Kent is said to have an infection rate of 500 per 100,000 people. 

Does that appear mathematically logical to you? Yes it is, but it is statistically indefensible because the sample is not in any way representative of the full population. The people being summoned or presenting for Covid testing are far more likely to test positive than a genuine random sample. Secondly, as mentioned, the PCR test is gaining an intractable reputation for returning false positives. The implications for reporting falsely high rates are very disturbing. 

Concluding with a personal perspective, I do not have a major problem with Professor Ferguson and all his sycophants. They should be left to rot away in academia where they belong. The real culprits are the ones that listen to them (and react with grotesque knee-jerk policies) without ever challenging the fundamental basis of their calculations. 

Footnote:

A reader has pointed out that the mathematical assumptions contained in my article concerning the infection rates (not the R number) may be incorrect. He asserts that if you do the maths on the number of cases per area, the numbers published are based on the number of cases per area (in the last 7 days) and dividing this by the total population. He tried the calculation on his area and it seemed (roughly) to work. I welcome the constructive criticism and stand corrected. But one further point to consider. If the official rates being published are based simply on the number of cases detected in the last seven days divided by the entire population of a region, then that is basically a (positive) case-counting exercise and is also statistically suspect to some extent. Because the proportion of negative test results are ignored, no matter how many there are. But I thank our reader for his response. I think a key point from my article is that the official statistics can be misleading and that too many powerful and influential figures just accept them at face value, so from my perspective the more debate and the more transparency the better.

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Bill Wright
Bill Wright is a freelance lecturer and a proud father of four. He is not aligned with any political party or cause except freedom.

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